Perfect nonlinear functions and cryptography

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Perfect nonlinear functions and cryptography. / Blondeau, Celine; Nyberg, Kaisa.

In: Finite Fields and Their Applications, Vol. 32, No. March, 2015, p. 120-147.

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Blondeau, Celine ; Nyberg, Kaisa. / Perfect nonlinear functions and cryptography. In: Finite Fields and Their Applications. 2015 ; Vol. 32, No. March. pp. 120-147.

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@article{a3ce54ab51d64545985774e2848bdad7,
title = "Perfect nonlinear functions and cryptography",
abstract = "In the late 1980s the importance of highly nonlinear functions in cryptography was first discovered by Meier and Staffelbach from the point of view of correlation attacks on stream ciphers, and later by Nyberg in the early 1990s after the introduction of the differential cryptanalysis method. Perfect nonlinear (PN) and almost perfect nonlinear (APN) functions, which have the optimal properties for offering resistance against differential cryptanalysis, have since then been an object of intensive study by many mathematicians. In this paper, we survey some of the theoretical results obtained on these functions in the last 25 years. We recall how the links with other mathematical concepts have accelerated the search on PN and APN functions. To illustrate the use of PN and APN functions in practice, we discuss examples of ciphers and their resistance to differential attacks. In particular, we recall that in cryptographic applications suboptimal functions are often used.",
keywords = "Perfect nonlinear functions, PN functions, Almost perfect nonlinear functions, APN functions, Differential uniformity, Nonlinearity, Differential cryptanalysis",
author = "Celine Blondeau and Kaisa Nyberg",
note = "VK: Kaisa Nyberg; Nyberg, K.; CRYPTO",
year = "2015",
doi = "10.1016/j.ffa.2014.10.007",
language = "English",
volume = "32",
pages = "120--147",
journal = "Finite Fields and Their Applications",
issn = "1071-5797",
publisher = "Academic Press Inc.",
number = "March",

}

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TY - JOUR

T1 - Perfect nonlinear functions and cryptography

AU - Blondeau, Celine

AU - Nyberg, Kaisa

N1 - VK: Kaisa Nyberg; Nyberg, K.; CRYPTO

PY - 2015

Y1 - 2015

N2 - In the late 1980s the importance of highly nonlinear functions in cryptography was first discovered by Meier and Staffelbach from the point of view of correlation attacks on stream ciphers, and later by Nyberg in the early 1990s after the introduction of the differential cryptanalysis method. Perfect nonlinear (PN) and almost perfect nonlinear (APN) functions, which have the optimal properties for offering resistance against differential cryptanalysis, have since then been an object of intensive study by many mathematicians. In this paper, we survey some of the theoretical results obtained on these functions in the last 25 years. We recall how the links with other mathematical concepts have accelerated the search on PN and APN functions. To illustrate the use of PN and APN functions in practice, we discuss examples of ciphers and their resistance to differential attacks. In particular, we recall that in cryptographic applications suboptimal functions are often used.

AB - In the late 1980s the importance of highly nonlinear functions in cryptography was first discovered by Meier and Staffelbach from the point of view of correlation attacks on stream ciphers, and later by Nyberg in the early 1990s after the introduction of the differential cryptanalysis method. Perfect nonlinear (PN) and almost perfect nonlinear (APN) functions, which have the optimal properties for offering resistance against differential cryptanalysis, have since then been an object of intensive study by many mathematicians. In this paper, we survey some of the theoretical results obtained on these functions in the last 25 years. We recall how the links with other mathematical concepts have accelerated the search on PN and APN functions. To illustrate the use of PN and APN functions in practice, we discuss examples of ciphers and their resistance to differential attacks. In particular, we recall that in cryptographic applications suboptimal functions are often used.

KW - Perfect nonlinear functions

KW - PN functions

KW - Almost perfect nonlinear functions

KW - APN functions

KW - Differential uniformity

KW - Nonlinearity

KW - Differential cryptanalysis

UR - http://dx.doi.org/10.1016/j.ffa.2014.10.007

U2 - 10.1016/j.ffa.2014.10.007

DO - 10.1016/j.ffa.2014.10.007

M3 - Article

VL - 32

SP - 120

EP - 147

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

IS - March

ER -

ID: 2000676